Implementing the derivative in C/C++

Question

How is the derivative of a f(x) typically calculated programmatically to ensure maximum accuracy?

I am implementing the Newton-Raphson method, and it re

Answer 1

In addition to John D. Cooks answer above it is important not only to take into account the floating point precision, but also the robustness of the function f(x). For instance, in finance, it is a common case that f(x) is actually a Monte Carlo-simulation and the value of f(x) has some noise. Using a very small step size can in these cases severely degrade the accuracy of the derivative.